27 Jan
2017
27 Jan
'17
5:27 p.m.
The warmup to 538's weekly math puzzle asks how many ways Tetris pieces (tetrominos) can fill a 2x10 rectangle. (I'm assuming because of the context that reflections and rotations are considered different.) See https://fivethirtyeight.com/features/can-you-win-at-tetris-can-you-save-a-sp ecies/ The answer is 64 unless my program is busted. It's easy for my program to do other sized rectangles. For 2-by rectangles I get: size solutions 2x2 1 4x2 4 6x2 9 8x2 25 10x2 64 12x2 169 14x2 441 16x2 1156 18x2 3025 20x2 7921 The second column looks like the squares of the Fibonacci numbers. Is there an easy proof? -- Tom Duff. Uh, oh, we've got company.